D₃×GL(2,𝔽₃) #64203

order	288
automorphism	Aut(G) = C₂²×D₃×S₄ (order 576) · Inn(G) = D₃×S₄ · Out(G) = C₂²
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

Fitting	C₃×Q₈ ⋊ C₂×D₃
derived	C₃×SL(2,𝔽₃) ⋊ C₂²

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×S₄
commutator, cosocle, hypocenter	C₃×SL(2,𝔽₃)	C₂²
Fitting	C₃×Q₈	C₂×D₃
socle	C₂×C₃	C₂×S₄
LCS	G ▷ C₃×SL(2,𝔽₃)
UCS	C₁ ◁ C₂

109 conjugacy classes of subgroups.

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 24

A minimal faithful permutation representation — 2 generators on 11 points:

(1,2,8,3,4,7,6,5)(9,10,11);(2,5,8)(3,6,7)(10,11)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 851);